Mobius Stitch

Finally, we present a new stitch that we invented expressly for
use in helical mobius strips. The mobius stitch
(Figure 9)
has symmetry
about both horizontal and vertical axes. Moreover, every row appears
exactly the same. These properties allow the construction of a seamless
single-helix mobius strip
(Figure 10).
The strip has no point
irregularities except for the start and end of the yarn. In the
appendix
we discuss how to make this stitch and how to use it to make a mobius
strip.

Figure 9:
The mobius stitch is a one-row pattern with symmetry
about both horizontal and vertical axes.

Figure 10:
A helical mobius strip made from mobius stitch has no seams
and is composed of a single yarn.

The challenge to knit a better mobius strip has led us to study the
underlying topological principles of knitting. In future work, we plan to
make precise mathematical definitions of knittable fabric and study
symmetries of such fabrics.